The understanding of novae, the thermonuclear eruptions on the surfaces of white dwarf stars in binaries, has recently undergone a major paradigm shift. Though the bolometric luminosity of novae was long thought to arise directly from photons supplied by the thermonuclear runaway, recent gigaelectronvolt (GeV) gamma-ray observations have supported the notion that a significant portion of the luminosity could come from radiative shocks. More recently, observations of novae have lent evidence that these shocks are acceleration sites for hadrons for at least some types of novae. In this scenario, a flux of neutrinos may accompany the observed gamma rays. As the gamma rays from most novae have only been observed up to a few GeV, novae have previously not been considered as targets for neutrino telescopes, which are most sensitive at and above teraelectronvolt (TeV) energies. Here, we present the first search for neutrinos from novae with energies between a few GeV and 10 TeV using IceCube-DeepCore, a densely instrumented region of the IceCube Neutrino Observatory with a reduced energy threshold. We search both for a correlation between gamma-ray and neutrino emission as well as between optical and neutrino emission from novae. We find no evidence for neutrino emission from the novae considered in this analysis and set upper limits for all gamma-ray detected novae.